The number of chickens to the number of ducks on a farm was 6: 5. After 63 ducks were sold, there were 3 times as many chickens as ducks left. How many chickens and ducks were there altogether on the farm in the end?

Question

Isaiah Anthony · Accepted Answer

Total chickens and ducks in the end are #168# in number.

Let #6x and 5x# be the numbers of chickens and ducks were on the farm. After #63# ducks were sold , remaining ducks were #(5x-63)# are in number. Now by condition , #6x:(5x-63) =3:1 or (6x)/(5x-63)=3/1 or 6x=15x-189 or 9x=189 or x=189/9=21# Total number of chickens and ducks in the end are #(6x)+(5x-63)=11x-63=11*21-63=231-63=168# in number.[Ans]

Eli Assouline · Answer

undefined Let the number of chickens be represented by $6x$ and the number of ducks be represented by $5x$. After selling 63 ducks, there were $5x - 63$ ducks left. Given that there were 3 times as many chickens as ducks left, the number of chickens left is $3(5x - 63)$. Since the ratio of chickens to ducks is $6:5$, we can set up the equation $\frac{3(5x - 63)}{6x} = \frac{3}{5}$. Solving this equation, we find $x = 35$. Therefore, the number of chickens left is $3(5 \times 35 - 63) = 252$ and the number of ducks left is $5 \times 35 - 63 = 112$. Thus, the total number of chickens and ducks left on the farm is $252 + 112 = 364$.